Factor. 4z^2 - 25 ______

Recognize as Difference of Squares: Determine the appropriate method to factor 4z^2 - 25. We recognize this expression as a difference of squares because it is in the form a^2 - b^2, where both terms are perfect squares and they are subtracted from each other.Identify Squares in Expression: Identify the terms in the expression 4z^2 - 25 as squares. 4z^2 can be written as (2z)^2 because 2z * 2z = 4z^2. 25 can be written as 5^2 because 5 * 5 = 25. So, 4z^2 - 25 is in the form (2z)^2 - 5^2.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Using this formula, we can write (2z)^2 - 5^2 as (2z - 5)(2z + 5).Write Final Factored Form: Write the final factored form of the expression. The factored form of 4z^2 - 25 is (2z - 5)(2z + 5).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4z^2 - 25

Recognize as Difference of Squares: Determine the appropriate method to factor $4z^2 - 25$ . We recognize this expression as a difference of squares because it is in the form $a^2 - b^2$ , where both terms are perfect squares and they are subtracted from each other.
Identify Squares in Expression: Identify the terms in the expression $4z^2 - 25$ as squares. $\newline$ $4z^2$ can be written as $(2z)^2$ because $2z \times 2z = 4z^2$ . $\newline$ $25$ can be written as $5^2$ because $5 \times 5 = 25$ . $\newline$ So, $4z^2 - 25$ is in the form $(2z)^2 - 5^2$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using this formula, we can write $(2z)^2 - 5^2$ as $(2z - 5)(2z + 5)$ .
Write Final Factored Form: Write the final factored form of the expression. $\newline$ The factored form of $4z^2 - 25$ is $(2z - 5)(2z + 5)$ .